Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Please help me to solve the differential equation $$y''=\frac{1}{y^2}$$

Thank you very much!

share|improve this question
    
Try a solution of the form $y=at^b$, where $a$ and $b$ are constants. Use the diffeq to find $a$ and $b$. The solution can then be generalized by the substitution $t\rightarrow t+c$. –  Ben Crowell Oct 3 '12 at 15:20

1 Answer 1

A start: The following is a standard trick. Multiply both sides by $y'$. Then the new left side is the derivative of $(1/2)(y')^2$ and the new right side is the derivative of $-1/y$. It follows that $$\frac{1}{2}(y')^2= -\frac{1}{y}+C$$ for some constant $C$. Solve for $y'$. You will get a couple of separable first-order differential equations.

share|improve this answer
3  
Physically, the diffeq can be interpreted as Newton's second law for a charged particle in the field of a second, like charge fixed at y=0. The method in your answer can be interpreted as a statement of conservation of energy. –  Ben Crowell Oct 3 '12 at 15:17

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.